Since then, the movement has spiraled into a volatile and dangerous crisis with no clear endgame. Support for protesters is fast waning, as days of violent clashes between activists, their opponents and police overshadow the movement. Vast differences over political reforms divide the students and the government. Key thoroughfares remain closed. Some protesters are digging in for the long haul at the main occupation zone, while others fight to retake ground lost to police.

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Against this backdrop, a government offer to negotiate with students appears highly unlikely to resolve the largest uprising since the former British colony returned to Chinese control 17 years ago.

"The endgame is nowhere in sight," said Willy Lam, a China expert at the Chinese University of Hong Kong. "Short of using a high degree of force, which might exacerbate dissatisfaction among the public, it looks like neither Beijing nor the Hong Kong government has what it takes to defuse the crisis."

Here are three key questions as the democracy protests continue to unfold:

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Q: WHAT IS THE HONG KONG GOVERNMENT'S STRATEGY?

A: Hong Kong authorities have been inconsistent both in handling the students' call for political reform and in tactics to clear the streets.

The city's highly unpopular leader, Chief Executive Leung Chun-ying — known as CY — angered protesters when he abruptly called off scheduled talks last week, saying a constructive outcome was unlikely. He then revived the proposal for talks a week later, amid soaring tensions and public anger over a video showing police beating a handcuffed protester.

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Even if the talks materialize, chances that they could resolve the deadlock quickly are slim. Leung repeatedly has said that Beijing will not give in to the students' demand to open up nominations for the city's inaugural direct election in 2017, and he has little wiggle room to offer compromises to the students.

"At this stage, Beijing is running the show. Beijing is dictating ways and means that it hopes the Hong Kong government will take to defuse the crisis," Lam said.

Meanwhile, Hong Kong's police appear entirely unprepared as they face a level of civil unrest not seen in the territory for decades.

A heavy-handed strategy of unleashing tear gas to disperse protesters on Sept. 28 and detaining student leaders backfired, drawing more supporters to the streets.

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Police then veered toward a softer approach, leaving the protest zones alone. This week they carried out surprise pre-dawn operations to retake parts of the streets — including clearing out the second-biggest encampment, in blue-collar Mong Kok — but those actions appear to have triggered a backlash from angry protesters. Hundreds returned to Mong Kok on Friday, leaving the area convulsed in chaos for hours as police tried to hold back the crowds.

The volatility and Leung's ineffective leadership are putting huge pressure on police to maintain order, said Steve Vickers, former head of intelligence with the colonial-era Royal Hong Kong Police Force, who now runs his own risk consultancy.

"The absence of any dialogue between the government and the public puts the police in a very exposed position," he said. "The inability of the Hong Kong government to directly make decisions is exacerbating the situation. What I'm saying is CY's not fully in charge."

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With Beijing appearing to want to avoid both bloodshed and a compromise with the student leaders, Lam said, "we have the making of a stalemate."

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Q: WHERE DOES THE PROTEST MOVEMENT STAND NOW?

A: From the start, a key feature of the protests has been their amorphous and organic nature. Three groups at the heart of the movement have rallied the crowds and led efforts to negotiate protesters' demands with the government, but there's no central leadership. Many taking part say the groups, headed by students and a law professor, do not represent them.

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That spontaneity appealed to many supporters, but it's become clear that the movement is unraveling at the edges and losing its unity of purpose.

As the standoff drags on, factions of more radical protesters are breaking off from the peaceful sit-ins at the main protest zone. For several nights in a row, large, rowdy crowds have stepped up their tactics to gain control of streets, scuffling with riot police. Others responded to calls on social media for flash mobs and what police condemned as "guerrilla tactics," sporadically rushing into traffic to dump barriers in the road before running away.

Most protesters say they want the movement to stay peaceful, and some are frustrated by the divisions among activists.

The video of police officers kicking a handcuffed protester — and images of police dragging activists away and aiming pepper spray at protesters' faces — have ignited even more volatility.

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On Thursday, student leaders urged protesters not to let anger at police distract from the movement's core purpose, or drive more ugly scenes that would spoil the movement's public image.

"We came here to protest, not to let out our emotions," Joshua Wong, an 18-year-old student leader, told protesters.

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Q: WHAT ARE THE LIKELY OUTCOMES?

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A: The Hong Kong government now faces myriad scenarios, none of them particularly palatable.

Both sides could try to move forward on talks based on minor compromises. Officials hinted Thursday that there could be room for maneuvering over how a committee that nominates Hong Kong's leader is picked, and that changes to elections could take place after 2017.

"If we don't do it in 2017, we could try to do it in 2022," Leung said.

The students could also be placated by Leung's resignation, though it's unlikely that Chinese President Xi Jinping would allow that, given his hard-line stance on dissent in China's other outlying regions, such as Tibet.

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In the shorter term, authorities could continue trying to wait the students out while police clear more protest zones in surprise raids. The strategy could be used to shut down the third and smallest site, in the Causeway Bay shopping district, where as few as 30 protesters were occupying about 100 meters (yards) of road on Friday morning.

But chances of success are less certain at the main site in Admiralty, a sprawling zone filled with tents, banners and protest art.

Vickers said the single biggest risk in the days ahead is the escalation of clashes between the protesters and their opponents, including triads, or criminal gangs who are widely suspected of being paid by shadowy pro-Beijing groups to stir up trouble.

"Police are going to be caught between the two groups, and that is not a nice place to be," he said.